Abstract: Among the possible explanations for Dark Matter, in the last years the WIMP candidate has been the main candidate to look for, given the feasibility of its experimental search (direct and indirect detection, and collider searches). In the last years, the community has been discussing the role of effective field theories and simplified models with regard to this issue. I will present some new results on the use of EFT for collider searches, and the crucial issues of complementarity of DM searches and internal consistency within simplified models.